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maths problems-degrees of freedom associated

Question # 00008232
Subject: Mathematics
Due on: 02/28/2014
Posted On: 02/10/2014 10:08 AM

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1. Calculate the degrees of freedom associated with a small-sample test of hypothesis for (?1 - ?2), assuming ?12 = ?22 and n1 = n2 = 16.


2. Calculate the degrees of freedom associated with a small-sample test of hypothesis for (?1 - ?2), assuming ?12 ? ?22 and n1 = 13, n2 = 12, s1 = 1.3, s2 = 1.5.


3. In a controlled laboratory environment, a random sample of 10 adults and a random sample of 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The data are summarized below:

Sample Mean Sample Variance
Adults (1) 77.5° F 4.5
Children (2) 74.5°F 2.5


Suppose that the psychologist decides to construct a 99% confidence interval for the difference in mean comfortable room temperatures instead of proceeding with a test of hypothesis. The 99% confidence interval turns out to be (-2.9, 3.1). Select the correct statement.
It cannot be concluded at the 99% confidence level that there is actually a difference between the true mean comfortable room temperatures for the two groups.
It can be concluded at the 99% confidence level that the true mean comfortable room temperature is between -2.9 and 3.1.
It can be concluded at the 99% confidence level that the true mean comfortable room temperature for children exceeds that for adults.
It can be concluded at the 99% confidence level that the true mean room temperature for adults exceeds that for children.


4. The owners of an industrial plant want to determine which of two types of fuel (gas or electricity) will produce more useful energy at a lower cost. The cost is measured by plant investment per delivered quad ($ invested /quadrillion BTUs). The smaller this number, the less the industrial plant pays for delivered energy. Suppose we wish to determine if there is a difference in the average investment/quad between using electricity and using gas. Our null and alternative hypotheses would be:


5. A researcher is investigating which of two newly developed automobile engine oils is better at prolonging the life of an engine. Since there are a variety of automobile engines, 20 different engine types were randomly selected and were tested using each of the two engine oils. The number of hours of continuous use before engine breakdown was recorded for each engine oil. Based on the information provided, what type of analysis will yield the most useful information?
Independent samples comparison of population means.
Independent samples comparison of population proportions.
Matched pairs comparison of population means.
Matched pairs comparison of population proportions.


6. We are interested in comparing the average supermarket prices of two leading colas. Our sample was taken by randomly selecting eight supermarkets and recording the price of a six-pack of each brand of cola at each supermarket. The data are shown in the following table:
Price
Supermarket Brand 1 Brand 2 Difference
1 $2.25 $2.30 $-0.05
2 2.47 2.45 0.02
3 2.38 2.44 -0.06
4 2.27 2.29 -0.02
5 2.15 2.25 -0.10
6 2.25 2.25 0.00
7 2.36 2.42 -0.06
8 2.37 2.40 -0.03
x1 = 2.3125
s1 = 0.1007 x2 = 2.3500
s2 = 0.0859 d = -0.0375
sd = 0.0381
Find a 98% confidence interval for the difference in mean price of brand 1 and brand 2.


7. An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 40 recently hired sales trainees were randomly assigned to one of 10 different "home rooms" - four trainees per room. Each room is identical except for wall color, with 10 different colors used. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the 10 room colors. At the end of the training program, the attitude of each trainee was measured on a 100-pt. scale (the lower the score, the poorer the attitude). How many treatments are in this experiment?



9. In a study to determine the least amount of time necessary to clean an SUV while maintaining a high quality standard, the owner of a chain of car washes designed an experiment where 20 employees were divided into four groups, each with five members. Each member of each group was assigned an SUV to clean within a certain time limit. The time limits for the groups were 20 minutes, 25 minutes, 30 minutes, and 35 minutes. After the time limits for each group had expired, the owner inspected each SUV and rated the quality of the cleaning job on a scale of 1 to 10. What are the factor levels for this experiment?



10. Given that the sum of squares for error (SSE) for an ANOVA F-test is 12,000 and there are 40 total experimental units with eight total treatments, find the mean square for error (MSE).

Tags aociated freedom problemsdegrees maths room mean confidence engine comfortable brand population comparison difference determine temperature psychologist sample time minutes true level concluded aigned plant trainees industrial using randomly different interval group experiment children test

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